Magma V2.20-10 Tue Mar 3 2015 21:01:28 on mathcompprd01 [Seed = 3964572440]
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Loading startup file "/home/eobr007/.magma.startup"
Loading "sign.m"
>
> n := 6;
> G := PermutationGroup ("3A6", 1);
> p := 5;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are [ 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree = 6 Defining field size = 5
Order of generators [ 2, 4, 4, 2 ]
Composition Factors of G is
G
| Alternating(6)
*
| Cyclic(3)
*
| Cyclic(2)
*
| Cyclic(2)
1
Refined bound on degree is 7
Order of G is 4320
... #O is now 432
... #O is now 1512
... #O is now 3672
... #O is now 5832
... #O is now 7992
... #O is now 10152
... #O is now 10872
... #O is now 11592
Proved no regular orbit
========================================
Input degree = 6 Defining field size = 5
Order of generators [ 2, 4, 2 ]
Composition Factors of G is
G
| Alternating(6)
*
| Cyclic(3)
*
| Cyclic(2)
1
Refined bound on degree is 7
Order of G is 2160
... #O is now 1080
... #O is now 2160
... #O is now 3240
... #O is now 4320
... #O is now 4680
... #O is now 5760
... #O is now 6120
... #O is now 7200
... #O is now 8280
... #O is now 9360
... #O is now 9720
... #O is now 10800
... #O is now 11016
... #O is now 11286
... #O is now 11646
... #O is now 11862
... #O is now 12942
... #O is now 13212
... #O is now 13572
Proved no regular orbit
========================================
Input degree = 6 Defining field size = 5
Order of generators [ 2, 4 ]
Composition Factors of G is
G
| Alternating(6)
*
| Cyclic(3)
1
Refined bound on degree is 6
Order of G is 1080
Found regular orbit
========================================
>
> n := 7;
> G := PermutationGroup ("3A7", 1);
> p := 5;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are [ 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree = 6 Defining field size = 5
Order of generators [ 3, 5, 4, 2 ]
Composition Factors of G is
G
| Alternating(7)
*
| Cyclic(3)
*
| Cyclic(2)
*
| Cyclic(2)
1
Vector space too small -- no regular orbit
========================================
Input degree = 6 Defining field size = 5
Order of generators [ 3, 5, 2 ]
Composition Factors of G is
G
| Alternating(7)
*
| Cyclic(3)
*
| Cyclic(2)
1
Refined bound on degree is 8
Order of G is 15120
... #O is now 630
Proved no regular orbit
========================================
Input degree = 6 Defining field size = 5
Order of generators [ 3, 5 ]
Composition Factors of G is
G
| Alternating(7)
*
| Cyclic(3)
1
Refined bound on degree is 7
Order of G is 7560
... #O is now 2520
... #O is now 5040
... #O is now 5670
... #O is now 7182
... #O is now 7812
... #O is now 9324
Proved no regular orbit
========================================
>
> n := 6;
> G := PermutationGroup ("3S6", 1);
> p := 5;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are [ 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree = 6 Defining field size = 5
Order of generators [ 2, 5, 4, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(6)
*
| Cyclic(3)
*
| Cyclic(2)
*
| Cyclic(2)
1
Refined bound on degree is 7
Order of G is 8640
... #O is now 4320
... #O is now 4752
... #O is now 5292
... #O is now 5832
... #O is now 6264
... #O is now 10584
Proved no regular orbit
========================================
Input degree = 6 Defining field size = 5
Order of generators [ 2, 5, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(6)
*
| Cyclic(3)
*
| Cyclic(2)
1
Refined bound on degree is 7
Order of G is 4320
... #O is now 1080
... #O is now 3240
... #O is now 5400
... #O is now 5760
... #O is now 6120
... #O is now 8280
... #O is now 9360
... #O is now 9720
... #O is now 11880
Proved no regular orbit
========================================
Input degree = 6 Defining field size = 5
Order of generators [ 2, 5 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(6)
*
| Cyclic(3)
1
Refined bound on degree is 7
Order of G is 2160
... #O is now 1080
Found regular orbit
========================================
>
> n := 7;
>
> G := PermutationGroup ("3S7", 1);
> p := 5;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are [ 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree = 6 Defining field size = 5
Order of generators [ 2, 6, 4, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(3)
*
| Cyclic(2)
*
| Cyclic(2)
1
Vector space too small -- no regular orbit
========================================
Input degree = 6 Defining field size = 5
Order of generators [ 2, 6, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(3)
*
| Cyclic(2)
1
Vector space too small -- no regular orbit
========================================
Input degree = 6 Defining field size = 5
Order of generators [ 2, 6 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(3)
1
Refined bound on degree is 8
Order of G is 15120
... #O is now 1512
Proved no regular orbit
========================================
>
> G := PermutationGroup ("3A7", 1);
> p := 7;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are [ 6, 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree = 6 Defining field size = 7
Order of generators [ 3, 5, 2 ]
Composition Factors of G is
G
| Alternating(7)
*
| Cyclic(3)
*
| Cyclic(2)
1
Refined bound on degree is 7
Order of G is 15120
... #O is now 7560
... #O is now 15120
... #O is now 18900
... #O is now 22680
... #O is now 24570
... #O is now 27090
... #O is now 34650
... #O is now 42210
... #O is now 49770
... #O is now 52290
... #O is now 54810
... #O is now 62370
... #O is now 69930
... #O is now 71820
... #O is now 79380
... #O is now 80640
... #O is now 88200
... #O is now 91980
... #O is now 94500
... #O is now 98280
... #O is now 100170
... #O is now 103950
Proved no regular orbit
========================================
Input degree = 6 Defining field size = 7
Order of generators [ 3, 5 ]
Composition Factors of G is
G
| Alternating(7)
*
| Cyclic(3)
1
Refined bound on degree is 7
Order of G is 7560
... #O is now 3780
... #O is now 7560
... #O is now 9450
... #O is now 10710
... #O is now 11340
... #O is now 12285
... #O is now 13545
... #O is now 17325
... #O is now 21105
... #O is now 24885
... #O is now 28665
... #O is now 32445
... #O is now 33075
... #O is now 36855
... #O is now 40635
... #O is now 44415
... #O is now 45360
... #O is now 49140
... #O is now 51030
... #O is now 54810
... #O is now 58590
... #O is now 62370
... #O is now 63315
... #O is now 63945
... #O is now 64890
... #O is now 68670
... #O is now 70560
... #O is now 72450
... #O is now 76230
... #O is now 76860
... #O is now 80640
... #O is now 81396
... #O is now 82656
... #O is now 86436
... #O is now 88326
... #O is now 89082
... #O is now 90027
... #O is now 90972
... #O is now 91917
... #O is now 95697
... #O is now 96957
... #O is now 98217
... #O is now 100107
... #O is now 103887
... #O is now 105147
... #O is now 106407
... #O is now 107163
... #O is now 109053
... #O is now 109998
... #O is now 110628
Proved no regular orbit
========================================
Consider the following repn 2
Input degree = 6 Defining field size = 7
Order of generators [ 3, 5, 2 ]
Composition Factors of G is
G
| Alternating(7)
*
| Cyclic(3)
*
| Cyclic(2)
1
Refined bound on degree is 7
Order of G is 15120
... #O is now 7560
... #O is now 15120
... #O is now 17640
... #O is now 25200
... #O is now 28980
... #O is now 32760
... #O is now 34650
... #O is now 42210
... #O is now 49770
... #O is now 57330
... #O is now 64890
... #O is now 68670
... #O is now 70182
... #O is now 73962
... #O is now 75852
... #O is now 83412
... #O is now 85302
... #O is now 86562
... #O is now 88452
... #O is now 92232
... #O is now 94752
... #O is now 97272
... #O is now 97398
... #O is now 98028
... #O is now 105588
Proved no regular orbit
========================================
Input degree = 6 Defining field size = 7
Order of generators [ 3, 5 ]
Composition Factors of G is
G
| Alternating(7)
*
| Cyclic(3)
1
Refined bound on degree is 7
Order of G is 7560
... #O is now 3780
... #O is now 7560
... #O is now 8820
... #O is now 12600
... #O is now 16380
... #O is now 20160
... #O is now 21420
... #O is now 22176
... #O is now 22302
... #O is now 23562
... #O is now 25452
... #O is now 27342
... #O is now 28287
... #O is now 30177
... #O is now 33957
... #O is now 37737
... #O is now 41517
... #O is now 45297
... #O is now 49077
... #O is now 49392
... #O is now 50652
... #O is now 54432
... #O is now 58212
... #O is now 58968
... #O is now 62748
... #O is now 66528
... #O is now 70308
... #O is now 71064
... #O is now 74844
... #O is now 78624
... #O is now 79884
... #O is now 80829
... #O is now 84609
... #O is now 85239
... #O is now 89019
... #O is now 89649
... #O is now 90909
... #O is now 92169
... #O is now 95949
... #O is now 96894
... #O is now 98784
... #O is now 100044
... #O is now 100800
... #O is now 102690
... #O is now 103950
... #O is now 104580
... #O is now 106470
... #O is now 107100
... #O is now 108990
... #O is now 109305
... #O is now 110565
Proved no regular orbit
========================================
>
Total time: 4.960 seconds, Total memory usage: 32.09MB